No, it is not possible to import reports created in the legacy version of Business Analyst Online to the new Business Analyst Online. Only sites created in the legacy application can be imported to the new application.
However, users can access the reports created in the legacy Business Analyst Online and choose to either save the previously created reports to their desktop or upload the reports to ArcGIS Online. To upload the reports to ArcGIS online, navigate to My Contents > Add Items, and save the legacy reports to the reports folder.
Note: Business Analyst Online is part of an ArcGIS Online organization subscription. This means that users get all of the sharing benefits built into ArcGIS Online.